A tank initially contains 200 L of brine with 30 kg of dissolved salt

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A tank initially contains 200 L of brine with 30 kg of dissolved salt. Brine with a concentration of 0.10 kg/L flows in at 8 L/min, while the mixture leaves at 5 L/min. The volume therefore increases by 3 L/min. Let Q(t)Q(t) be the amount of salt (in kg) in the tank tt minutes after the process begins. Which of the following expressions gives Q(t)Q(t)? (a) Q(t)=0.1(200+3t)+10(200200+3t)2/3Q(t)=0.1(200+3t)+10\left(\dfrac{200}{200+3t}\right)^{2/3} (b) Q(t)=0.1(200+3t)+10(200200+3t)5/3Q(t)=0.1(200+3t)+10\left(\dfrac{200}{200+3t}\right)^{5/3} (c) Q(t)=0.1(200+3t)+10(200+3t200)5/3Q(t)=0.1(200+3t)+10\left(\dfrac{200+3t}{200}\right)^{5/3} (d) Q(t)=0.8(200+3t)+10(200200+3t)5/3Q(t)=0.8(200+3t)+10\left(\dfrac{200}{200+3t}\right)^{5/3}

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